Case II. To find the Rate %, the Base and Percentage being given. What per cent. of ORAL EXERCISES. 1. 10 is 1? 5? 10? 20? 30? 40? 50? 60? 70 ? 80 ? 14. What per cent. is 2614, 29, 33, 363⁄4, of 175? * Answers: 4%, 5%, 13%, 15%, and 17%. The sum of thes: rates is 54, and 54% of 225 is 121.5, which is equal to the sum of the given percentages. In like manner the pupil may test for himself the correctness of his answers to the remaining questions Applications.-1. A boy buys an old pair of skates for 50¢ and sells them for 254. He then buys a pair for 254 which he sells for 504. What per cent. did he lose on the first pair? What per cent. did he gain on the second ? 2. If a dealer buys a hat for $3, and sells it for $4, what % does he gain? If he buys it for $4 and sells it for $3, what per cent. does he lose? 3. One hundred pounds of beef were sold for $6, having been bought @ 44 a lb. What per cent. profit? 4. A retail dealer in boots and shoes sold 50 pairs of boots for $300. They cost him $5 a pair. What rate per cent. did he gain? What per cent. would 5. A merchant bought goods for $500. he gain by selling them for $530? For $525? $540? For $560? For $575? For $600 ? For $600? 6. The price of a single ticket from Glenwood to New York city is 304, but 20 coupon tickets can be bought for $5. What per cent. is saved by buying coupon tickets? What per cent. is lost by buying single tickets? 7. 10% of a flock of sheep were killed by dogs; 63% of the rest were lost; 33% of the remaining number were sold, and 28 then remained. What was the original number? 8. At harvest time a farmer sold 60 bushels of wheat, which was 25% of the quantity he sent to mill, and what he sent to mill was 40% of what he kept over till the next spring. How many bushels had he at first? 9. When a merchant sold his goods for $261, he gained twice as much as he would have lost had he sold them for $207. What was his gain per cent.? (How many times the loss is the difference between $261 and $207 ?) 10. A grocer sold butter at 12% profit. more per pound, he would have gained 20%. cost him? Had he sold it for 24 What did 50 pounds Case III.-To find the Base, the Percentage and Rate % being given. ORAL EXERCISES. 1. Ten apples are 1/2 of how many apples? 50% of how many? 2. Eight bushels are % of how many bushels? 16% of how many? 3. 25 tons are 5% of how many tons? 25% of how many? EXERCISES. 5. 234 is 564% of what number? Solution. 23456 4.16 1%. 561 = = 416 100% or the number. Analysis. If 234 is 561/4% of any number, 1% of the number is such part of 234 as is found by dividing 234 by 561/4, which is 4.16 and 100%, or the number itself is 416 Ans. Or, since 561/4% of any number equals 9/16 of it, 234 is 9/16 of the number sought. If 234 is 9/16 of the number, the number itself is 16 times 1/9 of 234 = 416 Ans. Case IV.-To find the Base, the Rate % and the amount or difference being given. 1. The retail price of a certain article is 684. How much can the retailer pay for it to realize a gain of 33% ? 68¢ = 1333% of cost there is to be a gain of 33 1/3 per cent., 68¢ must be Explanation. If when the article sells for 68¢ 1333) 68 3 3 ·400 )2.04 .51=1% 51. cost 1333% of the cost; hence this problem is similar to that of Case III, which is to find the base, the percentage and rate % being given. Or, if when the article sells for 68¢ there is to be a gain of 331/3 %=1/3 of the cost, 68¢ must be 4/3 of the cost; hence the cost must be 3 times 1/4 of 68. 3 times 1/4 of 68 51¢ Ans. What number increased by 2. 10% of itself equals 110? 3. 75% of itself equals $420? 4. 62% of itself equals 89.372? 5. 21.5% of itself equals 32.562 ? 6. 83% of itself equals $87.12 ? 11. I am charged $2.50 for a is 33% less than it cost him. = Explanation. If when the book sells for $2.50 there is a loss of 33 1/3 %, the $2.50 must be 66 2/3 % of the cost; hence this problem also is similar to that of Case III. Or, since $2.50 is 662/3% or 2/3 of the cost, the cost must have been 3 times 1/2 of $2.50 = $3.75 Ans. What number diminished by 12. 5% of itself equals $6.65 ? 13. 5% of itself equals 19? 14. 20% of itself equals 80 ? 15. 9% of itself equals 9/10? = 6623)2.50 200 )7.50 .0375=1% 3.75 100% 16. 8712% of itself equals 10? 17. 163% of itself equals 95/18? 18. 5% of itself equals 67.95 ? 19.2% of itself equals 216.38? Note.-No special rule is needed for Case IV, the process of solution being the same as that of Case III. Applications.-1. William buys a penknife for 204 and sells it to James for 254, and James sells it to Fred for 204. What per cent. does William gain, and what per cent. does James lose? 2. If the 25 minutes of school time given to recesses are 83% of the daily session, how many hours in the session? 3. If a book is marked to be sold at 25% above cost, but it is sold at 20% below the marked price, what was the gain or loss per cent.? 4. If 80 pounds of coffee are exchanged for 120 pounds of sugar, what % is the coffee worth per pound more than the sugar? 5. What per cent. do I gain by selling an article for $3 for which I paid $2.25? What per cent. do I lose by buying an article for $3 and selling it for $2.25 ? 6. A drover sold a horse for $226, and thus gained 25%. What did he pay for him? 7. The assets of a business man are $135,700, which sum is 43% of his debts. What is his indebtedness? 8. A fruit dealer sold a lot of oranges for $337.50, which allowed him a profit of 12%. What did he pay for them? 9. A city lot was sold for $25,500, the gain on the cost being 325%. What was the cost? 10. A grocer sold 300 bushels of potatoes for $285, which was 163% less than he had paid for them. How much did they cost him per bushel? 11. A. sold goods at a gain of 18%. His profit was $29.70. How much did he sell them for? 12. By selling a lot of goods for $380, I gain 3 times the per cent. that would be gained by selling them for $340. What per cent. is gained in the latter case? ($380 - $340 = 2 times the gain.) 13. In the schools of a village yesterday there were 1235 pupils present, which was 95% of the whole number belonging. How many belonged to the schools? |